A monochromatic light of wavelength 800 ~nm is incident normally on a single slit of width 0.020 ~mm to produce a diffraction pattern on a screen placed 1 ~m away. Estimate the number of fringes obtained in Young's double slit experiment with slit separation 0.20 ~mm , which can be accommodated within the range of total angular spread of the central maximum due to single slit.

Step-by-step solution

The angular width of the central maximum in a single slit diffraction pattern is given by = 2 a , where = 800 10⁻⁹ m and a = 0.020 10⁻³ m . Substituting the values, = 2 800 10⁻⁹ 0.020 10⁻³ = 1600 10⁻⁹ 20 10⁻⁶ = 80 10⁻³ = 0.08 radians . In Young's double slit experiment, the angular fringe width is _ = d , where d = 0.20 10⁻³ m . Substituting the values, _ = 800 10⁻⁹ 0.20 10⁻³ = 800 10⁻⁹ 200 10⁻⁶ = 4 10⁻³ = 0.004 radians . The number of fringes N that can be accommodated within the central maximum is the ratio of th